Neural operators refined for better fine details and long stability
ReAl: Refine neural operators via aligning dynamical flow
Machine Learning
Summary
Many AI models that predict how physical systems change over time miss important small details or lose accuracy when predicting far into the future. The authors develop a method called ReAl that improves these predictions by first fixing missing fine details and then making sure predictions stay consistent over longer periods. This approach works with many existing models and helps them keep small structures and remain accurate even in complex, chaotic systems. Their tests show better detail and longer reliable forecasts.
What this means in practice
- •For computational fluid dynamics teams: Enhance fluid flow simulations by improving fine-scale structure prediction and long-term stability in AI surrogate models.
- •For weather prediction engineers: Increase accuracy in forecasting by refining neural models to better capture small-scale atmospheric details and maintain reliability over time.
Authors
Jing Xu, Zenglin Xu, Li Yi, Ruoxi Jiang, Yuan Qi
Abstract
Neural partial differential equation (PDE) surrogates trained with mean squared error (MSE) can capture dominant dynamics but often lose high-frequency information and fine-scale structures. Generative models (e.g., Flow Matching) can capture the distribution of fine-scale details, yet stochastic errors may accumulate during autoregressive rollouts and compromise long-term stability. To address these limitations, we introduce Refine and Align(ReAl), a model-agnostic plug-in that augments pretrained PDE surrogates to improve the reconstruction of high-frequency structures associated with complex physical phenomena. In the refinement stage, a conditional flow-matching model learns the residual distribution around the deterministic base prediction, recovering missing fine-scale structures while retaining the dominant dynamics. In the alignment stage, to mitigate the generative discrepancies amplified in the autoregressive rollout, particularly in chaotic systems, we generate multiple trajectories from the same input and reinforce the refiner with trajectory-level rewards, thereby achieving long-horizon dynamical alignment. Experiments across diverse surrogate architectures and PDE tasks demonstrate that ReAl consistently improves high-frequency fidelity, forecasting accuracy, and long-horizon stability.